# Fractions Calculator

The calculator will find (with steps shown) the sum, difference, product, and result of the division of fractions or mixed numbers. It will also convert fraction into decimal number and into improper fraction (if possible).

Enter fractions or

First fraction:

Second fraction:

The second fraction is needed for addition, subtraction, multiplication, division; but not for converting to decimal.
If you don't need a mixed number, leave the left cell empty.
If you need a negative fraction, write the minus sign in the left cell.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

## Solution

Your input: find the sum, difference, and product of two fractions, the result of the division; convert them into decimal.

The fractions are: $$2\frac{3}{7}$$$, $$\frac{5}{9}$$$

Convert $$2\frac{3}{7}$$$into an improper fraction. Rewrite $$2$$$ as $$\frac{14}{7}$$$Add the fractions: $$2\frac{3}{7}=\frac{14}{7}+\frac{3}{7}=\frac{17}{7}$$$ (we just add the numerators, since the denominators are equal).

So, $$2\frac{3}{7}=\frac{17}{7}$$$## Fractions addition Multiply the numerator and the denominator of the first fraction by $$9$$$: $$\frac{17}{7}=\frac{153}{63}$$$Multiply the numerator and the denominator of the second fraction by $$7$$$: $$\frac{5}{9}=\frac{35}{63}$$$Add the fractions: $$\frac{153}{63}+\frac{35}{63}=\frac{188}{63}$$$ (we just add the numerators, since the denominators are equal).

Convert into a mixed number.

Rewrite $$188$$$as $$2 \cdot 63+62$$$: $$\frac{188}{63}=\frac{2 \cdot 63+62}{63}=2\frac{62}{63}$$$So, $$\frac{188}{63}=2\frac{62}{63}$$$

## Fractions subtraction

Multiply the numerator and the denominator of the first fraction by $$9$$$: $$\frac{17}{7}=\frac{153}{63}$$$

Multiple the numerator and the denominator of the second fraction by $$7$$$: $$\frac{5}{9}=\frac{35}{63}$$$

Subtract fractions: $$\frac{153}{63}-\frac{35}{63}=\frac{118}{63}$$$(we just subtract the numerators, since the denominators are equal). Convert into a mixed number. Rewrite $$118$$$ as $$1 \cdot 63+55$$$: $$\frac{118}{63}=\frac{1 \cdot 63+55}{63}=1\frac{55}{63}$$$

So, $$\frac{118}{63}=1\frac{55}{63}$$$## Fractions multiplication Multiple the numerators and denominators: $$\frac{17}{7} \cdot \frac{5}{9}=\frac{85}{63}$$$

Convert into a mixed number.

Rewrite $$85$$$as $$1 \cdot 63+22$$$: $$\frac{85}{63}=\frac{1 \cdot 63+22}{63}=1\frac{22}{63}$$$So, $$\frac{85}{63}=1\frac{22}{63}$$$

## Fractions division

Multiple the first fraction by inverted second fraction: $$\frac{17}{7} \div \frac{5}{9}=\frac{17}{7} \cdot \frac{9}{5}=\frac{153}{35}$$$Convert into a mixed number. Rewrite $$153$$$ as $$4 \cdot 35+13$$$: $$\frac{153}{35}=\frac{4 \cdot 35+13}{35}=4\frac{13}{35}$$$

So, $$\frac{153}{35}=4\frac{13}{35}$$$## Decimal representation The decimal representation of $$\frac{17}{7}$$$ is $$2.42857142857143$$$The decimal representation of $$\frac{5}{9}$$$ is $$0.555555555555556$$$Answer: $$2\frac{3}{7}+ \left( \frac{5}{9} \right)=\frac{188}{63}=2\frac{62}{63}$$$

$$2\frac{3}{7}- \left( \frac{5}{9} \right)=\frac{118}{63}=1\frac{55}{63}$$$$$2\frac{3}{7} \cdot \left( \frac{5}{9} \right)=\frac{85}{63}=1\frac{22}{63}$$$

$$2\frac{3}{7} \div \left( \frac{5}{9} \right)=\frac{153}{35}=4\frac{13}{35}$$$The decimal representation of $$2\frac{3}{7}$$$ is $$2.42857142857143$$$The decimal representation of $$\frac{5}{9}$$$ is $$0.555555555555556$$\$